PHYSICS 9646/02. NANYANG JUNIOR COLLEGE Science Department JC 2 PRELIMINARY EXAMINATION Higher 2. Candidate Name. Tutor Name.

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1 NANYANG JUNIOR COLLEGE Science Department JC PRELIMINARY EXAMINATION Higher Candidate Name Class Tutor Name PHYSICS 9646/0 Paper Structured Questions 4 September hour 45 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and tutor name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question Total This document consists of 0 printed pages Nanyang Junior College NYJC 013 JC/Prelim/H/9646/0 [Turn over

2 Data speed of light in free space, c = 3.00 x 10 8 m s -1 permeability of free space, μ o = 4π x 10-7 H m -1 permittivity of free space, ε o = 8.85 x 10-1 Fm -1 elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, (1 / (36 π)) x 10-9 Fm -1 e = 1.60 x C h = 6.63 x J s u = 1.66 x 10-7 kg m e = 9.11 x kg m p = 1.67 x 10-7 kg molar gas constant, R = 8.31 J K -1 mol -1 the Avogadro constant, N A = 6.0 x 10 3 mol -1 the Boltzmann constant, k = 1.38 x 10-3 J K -1 gravitational constant, G = 6.67 x N m kg - acceleration of free fall, g = 9.81 m s - mulae uniformly accelerated motion, s = ut + ½at work done on/by a gas, hydrostatic pressure, v = u + as W = pδv p = Ρgh gravitational potential, = Gm / r displacement of particle in s.h.m. velocity of particle in s.h.m. mean kinetic energy of a molecule of an ideal gas resistors in series, resistors in parallel, electric potential, alternating current/voltage, transmission coefficient, radioactive decay, decay constant x = x o sin ωt v = v o cos ωt = x o x 3 E = kt R = R 1 + R + 1/R = 1/R 1 + 1/R + V = Q / 4πε o r x = x o sin ωt T α exp(-kd) 8 m U E where k = h x = x o exp (-λt) λ = t 1 NYJC 013 JC/Prelim/H/9646/0

3 3 1 (a) State the relation between force and momentum. ce is proportional (or equal) to the rate of change of momentum... [1] (b) A rigid bar of mass 450 g is held horizontally by two supports A and B, as shown in Fig Fig. 1.1 The support A is 45 cm from the centre of gravity C of the bar and the support B is 5 cm from C. A ball of mass 140 g falls vertically onto the bar such that it hits the bar at a distance of 50 cm from C, as shown in Fig The variation with time of the velocity of the ball before, during and after hitting the bar is shown in Fig. 1.. Fig. 1. NYJC 013 JC/Prelim/H/9646/0 [Turn over

4 4 the time that the ball is in contact with the bar, use Fig. 1. to determine (i) the magnitude of the change in momentum of the ball, p = 140 x 10-3 [5.4 ( 4.0)] = 1.3 kg m s -1 change in momentum =.. kg m s -1 [] (ii) the magnitude of the force exerted by the ball on the bar. ( )( ) ( )( ) N force by ball =.. N [] (c) Hence, calculate the magnitude of the force exerted on the bar by support A for the time that the ball is in contact with the bar. Taking moments about B, ( ) ( )( ) ( ) force by support A =.. N [] NYJC 013 JC/Prelim/H/9646/0

5 5 An unpowered artificial satellite of mass m has been placed in a stable orbit around the Sun in the same direction as that of the Earth. It is at a distance of 0.99R from the Sun, where R is the orbital radius of the Earth as shown in Fig..1. Sun 0.99R satellite Earth R Fig..1 (a) Ignore the very small force the satellite acts on the Earth. Show that the period of the Earth round the Sun T E is given by T E 4 R GM S 3/ where M S is the mass of the Sun. GMSM R GM R T E S E MR E ( ) T R ( ) T E 4 R GM S 3/ E [] GMSm (b) Show that the resultant force on the satellite is given by 0.99, given that the R mass of the Sun is 3.33 x 10 5 times the mass of Earth. MS G( ) m GM 5 Sm GMEm GMSm F x10 (0.99 R) (0.01 R) R R GMSm GMSm GMSm R R R [] NYJC 013 JC/Prelim/H/9646/0 [Turn over

6 6 (c) Hence determine the period of the satellite round the Sun in terms of the period of the Earth T E. GMSm 0.99 (0.99 )( ) m R R T GMS ( ) R R T 4 T R TE GMS Period of satellite = [] (d) Si c h i i g i g d h S i i, i i i q i i i m. Comment on the statement. The satellite is not in equilibrium because it has centripetal acceleration. Hence the resultant.. force is not zero. [1] 3 (a) State the principle of superposition.... [1] (b) Figure 3.1 shows a double slit S 1 and S emitting waves of amplitude A and of wavelength 590 nm. They are placed mm apart and at a distance of.70 m from a line XY. Point O is in the center of the fringe pattern. Two polarizers P 1 and P are placed in front of S 1 and S respectively. The polarizers are rotated such that a fringe pattern is observed along the line XY. S S mm S P 1 P.70 m Fig. 3.1 X O Y NYJC 013 JC/Prelim/H/9646/0

7 7 (i) Show that the fringe separation along the line XY is.00 mm. [1] (ii) On Fig. 3., ignoring diffraction effects, sketch the variation of intensity along the line XY. Label your values clearly on the axes. [] intensity X Y mm Fig. 3. (c) The polarizer P 1 is rotated 90 o along its plane. (i) Calculate the resultant amplitude at point O on the line XY in terms of A. amplitude = [1] NYJC 013 JC/Prelim/H/9646/0 [Turn over

8 8 (ii) Calculate the resultant amplitude at a point 1.00 mm from point O along the line XY in terms of A. amplitude = [1] (iii) Describe the appearance of the fringe pattern.... [1] 4 An ideal transformer has 5000 turns on its primary coil. It is used to convert a main supply of root mean square value of 30 V to an alternating voltage having a peak value of 1.0 V. (a) (i) Explain what is meant by root mean square value of 30 V [] (ii) Calculate the number of turns on the secondary coil. number of turns =.. [] NYJC 013 JC/Prelim/H/9646/0

9 9 (b) The secondary coil is connected in series with a resistor R. The variation with time t, in seconds, of the potential difference at the secondary coil is given by the expression V = 1.0 sin(380t) (i) Determine the frequency of the supply. frequency =.. Hz [1] (ii) To prevent overheating, the mean power dissipated in R must not exceed 300W. Calculate the minimum resistance of R. resistance =.. Ω [] 5 (a) A uniform magnetic field has constant flux density B. A straight wire of fixed length carries a current I at an angle θ to the magnetic field as shown in Fig Fig. 5.1 (i) Define the term magnetic flux density. It is the force per unit length experienced by a straight conductor carrying unit... current when the conductor is placed at right angles to the magnetic field. [1] NYJC 013 JC/Prelim/H/9646/0 [Turn over

10 10 (ii) The current I in the wire is changed, keeping the angle θ constant. On Fig. 5., sketch a graph to show the variation with the current I of the force F on the wire. [1] Fig. 5. (iii) The angle θ between the wire and the magnetic field is now varied. The current I is kept constant. On Fig. 5.3, sketch a graph to show the variation with angle θ of the force F on the wire. [1] Fig. 5.3 NYJC 013 JC/Prelim/H/9646/0

11 (b) Negative ions are travelling through a vacuum in a narrow beam. The ions enter a region of uniform magnetic field of flux density B and are deflected in a semi-circular arc, as shown in Fig. 5.

11 11 (b) Negative ions are travelling through a vacuum in a narrow beam. The ions enter a region of uniform magnetic field of flux density B and are deflected in a semi-circular arc, as shown in Fig detector uniform magnetic field beam of negative ions Fig. 5.4 The ions, travelling with speed m s -1, are detected at a fixed detector when the diameter of the arc in the magnetic field is 1.8 cm. (i) By reference to Fig. 5.4, state the direction of the magnetic field. Out... of the plane of the paper. [1] (ii) The ions have mass 0u and charge C. Show that the magnetic flux density is T. Explain your working. Since the magnetic force on the ions provide for its centripetal force, ( )( ) ( ) ( ) [] (iii) Ions of a larger mass with the same charge and speed as those in (b)(ii) are also present in the beam. On Fig. 5.4, sketch the path of these ions in the magnetic field of magnetic flux density T. [1] NYJC 013 JC/Prelim/H/9646/0 [Turn over

12 1 6 Fig. 6.1 shows a simple circuit. The resistance of the lamp is 0 Ω and it requires a minimum of 60 V to light up. 40 V Fig. 6.1 Fig. 6. shows how the current I through the light dependent resistor varies with the potential difference V across it when different intensities of light fall onto it. I / A W m W m W m W m - 0 W m - 0 V / V Fig. 6. NYJC 013 JC/Prelim/H/9646/0

13 13 (a) Calculate the current through the 30 Ω resistor when the potential difference across the lamp is 40 V. V I R A current = A [] (b) Explain how the above circuit can be used as a warning system for an environment which requires low intensity light. If the intensity of the light in the environment is high, the resistance of the light dependent resistor will be low. This will cause the potential difference across the.. lamp to be more than 50 V, causing the lamp to light up, indicating that the [] intensity of the light in the environment is high. NYJC 013 JC/Prelim/H/9646/0 [Turn over

14 14 (c) Using Fig. 6., determine the intensity of light which will produce a potential difference of 60 V across the lamp. Total resistance of parallel arrangement ( ) Resistance of L.D.R: R R 4 intensity of 5000 W m -. OR If the p.d across the lamp is 60 V, the p.d. across the L.D.R will be = 180 V. If we have the current flowing through the L.D.R when its p.d. is 180 V, we can look for the point on Fig. 6. and determine which graph and which ntensity. Total resistance of parallel arrangement ( ) Current flowing through the L.D.R: I A 8 From the graph, the graph which shows a current of 7.5 A at 180 V is the one with an intensity of 5000 W m -. intensity =.. W m - [3] NYJC 013 JC/Prelim/H/9646/0

15 15 7 Wind power can be used for the generation of electric power. Fig 7.1 and Fig 7. illustrate a particular type of wind turbine. hub drive shaft gearbox drive shaft generator generator housing Fig 7.1 Fig 7. Table 7.3 shows some information provided by the manufacturer. Table 7.3 Height of tower (ground to hub) 80 m Blade length 45 m Number of blades 3 Rated power 3 MW Voltage 650 V Frequency 50 Hz NYJC 013 JC/Prelim/H/9646/0 [Turn over

m [1] (ii) the area swept by the rotor blades Sweep area = π 45 = 6.36 103 m area =.

16 16 Fig 7.4 shows the wind turbine power curve provided by the manufacturer. Fig 7.4 (a) Using the information provided in Table 7.3, calculate (i) the height of the lowest point of the rotor above the ground, Height = = 35 m height =. m [1] (ii) the area swept by the rotor blades Sweep area = π 45 = m area =. m [1] (iii) the period of revolution of the rotor when the wind speed is 10 m s 1, given that the ratio of the speed of the blade tip to the wind speed is 7. Blade tip speed = 7 10 = 70 m s 1 Period = ( 45) / 70 = 4.0 s period =. s [] NYJC 013 JC/Prelim/H/9646/0

17 17 (b) (i) Discuss, with reasons, if the rated power of 3 MW is a fair value. The turbine is able to produce more than the rated power for wind speeds between 1 m s 1 and 5 m s 1. sites with wind speeds averaging above 1 m s 1, the rated power will be a fair value... [] (ii) The average monthly electrical energy consumption per household in Singapore is 470 kw h. Calculate the number of homes one wind turbine can serve when operating at the rated power. Power consumption per household = 470 (30 4) No of homes = = 4600 = 0.65 kw number of homes =. [] (c) (i) Using the information provided in Fig 7.4, obtain values for 1. the maximum power output, maximum power =. MW [1]. the wind speed for this power. wind speed =. m s 1 [1] (ii) The incident wind power E, which is the kinetic energy of the air incident on the rotor to turn the blades per unit time, is given by E = k L v 3 where L is the blade length of the turbine, v is the incident wind speed, and k is a constant of value 1.96 kg m 3 Calculate, for the turbine operating at maximum output power, the incident wind power. E = = J s -1 incident wind power =. W [1] NYJC 013 JC/Prelim/H/9646/0 [Turn over

18 18 (iii) Acc di g z L w, which i d iv d f m h i ci f c v i f mass and momentum, the maximum amount of the incident wind kinetic energy that can be captured by a wind turbine is 59.3%. Suggest one evidence that not all of the incident wind energy can be captured. The wind will still be moving, albeit at a lower speed, after passing through the... rotor. Thus it could not have lost all of its kinetic energy. [1] (iv) Calculate the efficiency of the wind turbine in converting the accessible kinetic energy to electrical energy when operating under the conditions stated in (i). Accessible wind power = efficiency =. % [] (d) The wind turbine, like most others, has a cut-out speed. This means that at high wind speeds, the gearbox disengages the generator from the rotor and the generator is no longer turned by the rotor. (i) Fig 7.4 to determine the cut-out speed. cut-out speed =. m s 1 [1] (ii) Suggest one reason why it is necessary to have a cut-out speed. The generators are designed to take a certain maximum electrical load.... Having a cut-out speed will prevent the circuit from being overloaded and [1] damaged. (e) Wind turbines are usually erected in wide open spaces. As such, they are vulnerable to (i) strong winds which may cause the rotor to rotate too fast and be damaged, and (ii) lightning which may strike the rotor, causing damage. each of the hazards mentioned, suggest how the risk of damage to the rotor may be minimized. (i) Strong winds Install brakes to resist rotation.... Turn the blades to face away from the wind. [1] (ii) Lightning = W Efficiency = / = 38% poor electrical conductor such as fiberglass for blades.... Install lightning rods taller than the turbine nearby. [1] NYJC 013 JC/Prelim/H/9646/0

19 19 8. Fig. 8.1 shows a coil (coil X). Fig. 8.1 A student winds another coil (coil Y) tightly around coil X. A changing e.m.f. in coil X induces an e.m.f. in coil Y. The student wishes to investigate how the e.m.f. V in coil Y depends on the frequency f of the current in coil X. It is suggested that V is directly proportional to f. Design a laboratory experiment to investigate the suggested relationship. You should draw a diagram, in the space provided below, showing the arrangement of your equipment. In your account you should pay particular attention to: (a) the procedure to be followed, (b) the measurements to be taken, (c) the control of variables, (d) the analysis of the data, (e) the safety precautions to be taken. Diagram NYJC 013 JC/Prelim/H/9646/0 [Turn over

20 NYJC 013 JC/Prelim/H/9646/0

21 [1] NYJC 013 JC/Prelim/H/9646/0 [Turn over

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level

www.xtremepapers.com UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Level *9061759643* PHYSICS 9702/41 Paper 4 A2 Structured Questions October/November 2012